theres nothing wrong with keeping a tasbih although it is also good to count dhikr on your right hand the Sunnah way. A tasbih(rosary) is brilliant because it actually reminds one to do dhikr in the first place whereas if one did'nt have one then one would be less likely to actually do dhikr or remember to do dhikr in the first place.
I personally have a metal counter which you can carry anywhere you go. You can get them from most Islamic shops and they are brilliant to carry everywhere so one never has to stop doing dhikrullah. it is also a brilliant reminder to do dhikr in the first place.
Here are dhikr's we can all do everyday:
Easy Dhikr which is light on the tongue but heavy on the scales!